Are they $\pi$ systems?

Question

I am not sure whether the following two systems are closed under finite intersections.

1. $\{(a,b):-\infty<a<b<\infty\}$: I do not think it is if I consider $(0,1)\cap(1,2)=\emptyset\notin \{(a,b):-\infty<a<b<\infty\}$.
2. $\{[a,b]:-\infty<a<b<\infty\}\cup\{\emptyset\}$: I do not think it is if I consider $[0,1]\cap[1,2]=\{1\}\notin \{[a,b]:-\infty<a<b<\infty\}\cup\{\emptyset\}$.

Am I right?